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This study focuses on studying the asymptotical stability analysis problem for discrete-time systems with time-varying delay. By utilising the S-procedure and an inequality technique, a novel delay-dependent stability criterion is derived in terms of two linear matrix inequalities. Since no slack variable is introduced, less decision variables are involved in the stability condition and the burden of numerical computation is thus reduced. It is also rigorously proved that the authors' result is less conservative than some recent ones. Furthermore, the developed approach is extended to address the stability analysis problem of delayed discrete-time systems with norm-bounded uncertainties. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results.